Numerical analysis of turbulent superstructures in thermal convection: Long-term dynamics by Lagrangian clustering and Markov state modeling

热对流中湍流上层结构的数值分析：通过拉格朗日聚类和马尔可夫状态建模进行长期动力学

• 批准号: 315181729
• 负责人: Professor Dr. Jörg Schumacher
• 金额: --
• 依托单位: Fachgebiet Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/315181729?language=en
• 关键词: Numerical; analysis; turbulent; superstructures; thermal

Large-scale patterns of the time-averaged velocity and temperature fields are found for turbulent convection in a horizontally extended layer. These patterns are termed turbulent superstructures and will be in the focus of the present proposal. We want to understand their dynamical origin from the weakly nonlinear regime, their importance for the turbulent heat transport and model transitions between different superstructure patterns in turbulence. Our investigations are based on massively parallel three-dimensional direct numerical simulations of turbulent Rayleigh-Benard convection in large-aspect-ratio domains that include very low and high Prandtl number cases. In order to answer the questions and to study the long-term evolution of superstructures, we will have to reduce the vast amount of degrees of freedom of the flow. This is done by (1) generalized Markov state models which are based on a long-term low-resolution flow trajectory in combination with short-term full-resolution ensemble simulations and (2) by (evolutionary) clustering in ensembles of Lagrangian tracer tracks. While method (1) gives transition probabilities between different macroscopic superstructure patterns, method (2) reveals the most persistent and longest-living Lagrangian coherent sets in the turbulent convection flow. The work is conducted together with colleagues from Fluid Mechanics, Computer Science and Applied Mathematics.

水平扩展层中湍流对流的时间平均速度场和温度场具有大尺度的分布。这些模式被称为湍流上层建筑，将是本提案的重点。我们想要了解它们的动力学起源，它们对湍流热传输的重要性，以及它们在湍流中不同超结构模式之间的模式转换。我们的研究是基于大宽高比区域内湍流Rayleigh-Benard对流的大规模并行三维直接数值模拟，其中包括很低和很高Prandtl数的情况。为了回答这些问题并研究上层建筑的长期演变，我们将不得不减少流动的巨大自由度。这是通过(1)基于长期低分辨率流动轨迹与短期全分辨率系综模拟相结合的广义马尔可夫状态模型来实现的，以及(2)通过在拉格朗日示踪轨迹系综中(进化)聚类来实现的。方法(1)给出了不同宏观超结构模式之间的转换概率，方法(2)揭示了湍流对流中持续时间最长、寿命最长的拉格朗日相干集。这项工作是与流体力学、计算机科学和应用数学的同事一起进行的。